Modern integrated circuits components often require a temperature sensor. A common way to measure the temperature in integrated circuits is to make use of the temperature dependence of the voltage drop across diodes. Often, a base-emitter diode is formed from a bipolar transistor for use in the temperature sensor.
FIG. 1 depicts a schematic diagram of a prior art temperature sensor circuit. In FIG. 1, a unity current I flows through the transistor T2 on the right side of the circuit, while a current of A times the unity current flows through the transistor T1 on the left side of the circuit. The base-emitter voltage of T1 differs from the base-emitter voltage of T2. The difference between both voltages is referred to as ΔVBE. ΔVBE is expressed by:
                              Δ          ⁢                                          ⁢                      V            BE                          =                              kT            q                    ·                      ln            ⁡                          (              A              )                                                          (                  Equation          ⁢                                          ⁢          1                )            
where k is the Boltzmann constant (1.38·10−23 J/K), T is the absolute temperature, and q is the elementary charge of an electron (1.6·10−19 As).
Since the voltage ΔVBE is proportional to absolute temperature, ΔVBE is well suited for use in measuring the temperature of the sensor. Consequently, temperature of the sensor can be determined by solving equation 1 for T resulting in:
                    T        =                                            q              ·              Δ                        ⁢                                                  ⁢                          V              BE                                            k            ·                          ln              ⁡                              (                A                )                                                                        (                  Equation          ⁢                                          ⁢          2                )            
The circuit depicted in FIG. 1 would provide accurate temperature measurements using ideal transistors having base resistance values R_B and emitter resistance values R_E of zero ohms. In actual bipolar transistors, however, the structure of the transistor includes an inherent and non-zero base resistance R_B and emitter resistance R_E. The resistance of the base is of particular concern with a typical value for R_B of approximately 10Ω to 3000Ω. The value of R_B changes, however, as corresponding temperature of the transistor changes. The temperature dependent value of the base resistance is expressed as RB(T). The inclusion of the base resistance produces a more complex equation expressed as:
                              Δ          ⁢                                          ⁢                      V            BE                          =                                            kT              q                        ·                          ln              ⁡                              (                A                )                                              +                                                    R                B                            ⁡                              (                T                )                                      ·            A            ·                                          I                c                                            β                ⁡                                  (                  T                  )                                                              -                                                    R                B                            ⁡                              (                T                )                                      ·                                          I                c                                            β                ⁡                                  (                  T                  )                                                                                        (                  Equation          ⁢                                          ⁢          3                )            
where Ic is the unity current and β(T) is the temperature-dependent current gain β of the transistor. Thus, the base resistance introduces multiple temperature dependent factors that affect the value of ΔVBE. In existing temperature sensors, the inherent base resistance produces an error of approximately ±0.5° C. in the output of the temperature sensor.
What is needed, therefore, is a circuit that reduces or eliminates the errors introduced by intrinsic resistances in the transistors in various applications including temperature sensing, reference voltage generation, and reference current generation.